So with the random packing I do agree that there will be small clusters that are within themselves close packed. It would be interesting to know the relative distribution, though it's clear that large areas of close packing would be less and less probable. Groups have used MRI scanning to probe what's actually going…

For spheres, 'close packing' with 12 nearest-neighbours is 74% space-filling, so eqv't to 1155/(pi()*.84^2)=385 balls in the 5 gallon bucket, but minus a few for inefficiencies at the sides - but you'd have to pack them in carefully to get there.
'Random close packing' is well studied because it has real implications…

Thanks for standing up for this, because I'm right here with you.
For an argument to be 'punching' both denies it being entirely objective truth, and implies a tone dividing rather than drawing together. Never mind the effect on the punchee, it's too easy for the puncher (and whoever they're standing up for) to…

If you haven't already mined them (and dependent on your appetite for radio panels shows), Dilemma and The 99p Challenge both are worth a shot.